JPH06302496A - Alignment method - Google Patents

Abstract

PURPOSE:To perform highly accurate alignment even when a wafer to be exposed has local nonlinear distortion. CONSTITUTION:The coordinates of sample shots SA(1)-SA(8) selected from exposing shots in a wafer W on a stage coordinate system (X, Y) are measured and the quantity of distortion in exposing shots ES (i, j) is calculated from the measured results. In response to the integrated value of the distortion quantities between the exposing shot ES (i, j) to be aligned and each sample shot SA (k), weight Wx (ijk) in the X-direction and weight Wy (ijk) in the Y-direction are given to each sample shot SA (k) and each exposing shot ES (i, j) is aligned by weighted EGA method using such weights.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention sequentially aligns each shot area of a wafer in an exposure apparatus which sequentially exposes a pattern of a reticle on each shot area of a wafer based on array coordinates calculated by statistical processing. The present invention relates to a positioning method suitable for use in some cases.

[0002]

2. Description of the Related Art When manufacturing a semiconductor device, a liquid crystal display device, a thin film magnetic head, or the like by a photolithography process, a pattern image of a photomask or reticle (hereinafter referred to as "reticle") is exposed through a projection optical system. A projection exposure apparatus is used that projects onto each shot area on a wafer coated with a material. In recent years, as a projection exposure apparatus of this type, a wafer is placed on a stage that is two-dimensionally movable, and the wafer is stepped by this stage.
Thus, a so-called step-and-repeat type exposure apparatus, particularly a reduction projection type exposure apparatus (stepper), which repeats the operation of sequentially exposing the pattern image of the reticle to each shot area on the wafer is frequently used.

For example, since a semiconductor element is formed by stacking multiple layers of circuit patterns on a wafer, when projecting and exposing the circuit patterns of the second and subsequent layers, the circuit patterns are already formed on the wafer. Further, it is necessary to accurately align each shot area with the pattern image of the reticle, that is, accurately align the wafer and the reticle. As a conventional wafer alignment method for a stepper or the like, the following enhanced global
An alignment (hereinafter referred to as "EGA") method has been used (see, for example, JP-A-61-44429).

In this EGA method, a plurality of shot areas (chip patterns) each including a positioning mark called a wafer mark are formed on the wafer, and these shot areas are set in advance on the wafer. It is regularly arranged based on the arranged coordinates. However, even if the wafer is stepped based on the designed array coordinate values (shot arrays) of a plurality of shot areas on the wafer, the wafer is not always accurately aligned due to the following factors.

(1) Remaining rotation error of wafer θ (2) Orthogonal error of stage coordinate system (or shot arrangement) w (3) Linear expansion and contraction (scaling) of wafer Rx, Ry (4) Wafer (center position) Offset (translation) O
x, Oy

At this time, the coordinate transformation of the wafer based on these four error amounts (six parameters) can be described by a linear transformation equation. Therefore, for a wafer in which a plurality of shot areas including wafer marks are regularly arranged, the coordinate value of the coordinate system (x, y) on the wafer as the sample coordinate system is set to the coordinate on the stage as the stationary coordinate system. The primary conversion model for converting into the coordinate value of the system (X, Y) is converted into six conversion parameters a to f.
Can be expressed as follows.

[0007]

[Equation 1]

The six conversion parameters a to f in this conversion formula can be obtained by, for example, the least square approximation method. In this case, in the design on the coordinate system (x, y) attached to each of the shot areas (hereinafter referred to as “sample shots”) selected from a plurality of shot areas (chip patterns) on the wafer. Coordinates of (x
1, y1), (x2, y2), ..., (Xn, yn) are aligned with a predetermined reference position (alignment). Then, the coordinate values (xM1, yM) in the coordinate system (X, Y) on the stage at that time
1), (xM2, yM2), ..., (xMn, yMn)
Is actually measured.

Further, the calculated array coordinates (xi, yi) (i = 1, ..., N) of the selected wafer marks are substituted into the above-mentioned linear transformation model to obtain the calculated array coordinates. (Xi, Yi) and the measured coordinate (x
The difference (Δx, Δy) from Mi, yMi) is considered as an alignment error. The one alignment error Δx is represented by, for example, the sum of (Xi-xMi) ² with respect to i, and the other alignment error Δy is represented by, for example, the sum of (Yi-yMi) ² with respect to i.

Then, the alignment errors .DELTA.x and .DELTA.y are sequentially partially differentiated with the six conversion parameters a to f, an equation is set so that the value becomes 0, and these six simultaneous equations are solved. For example, six conversion parameters a to f are obtained. After that, the alignment of each shot area of the wafer can be performed based on the array coordinates calculated by using the linear conversion equation having the conversion parameters a to f as coefficients.
Alternatively, when the approximation accuracy is not good in the primary conversion formula, the wafer may be aligned by using, for example, a second or higher order formula.

[0011]

In the prior art as described above, when the wafer to be exposed has a non-linear distortion, the residual error corresponding to the non-linear distortion becomes a positioning error. It was Therefore, the applicant of the present invention, as an alignment method in the case of such distortion, has a small distance from a shot reference area (hereinafter, referred to as an “exposure shot”) or a predetermined reference point in a wafer to be exposed. A weighted EGA method is proposed in which the influence of the nonlinear error due to the distortion is small.

In the weighted EGA method, a linear approximation of the weighting method is performed by weighting a sample shot having a smaller distance from a reference point (a center of distortion or the like) in an exposure shot or a wafer to be exposed, and performing linear approximation of the weighting method. After the correction components of the wafer offset, rotation, scaling, and orthogonality are obtained for each shot, the position of each exposure shot is set to the position obtained by correcting only those correction components, and exposure is performed. In this weighted EGA, the effect of distortion is simply said to be smaller for an exposure shot or a sample shot closer to a predetermined reference point. However, in reality, the amount of distortion depends on the distance between shots or the distance between the reference point. There are times when you don't. For example, when there is local distortion, the distortion may be large regardless of the distance between shots or the distance between the shot and the reference point. Therefore, even with the above-described weighted EGA method, there are cases where the positional deviation error due to the influence of nonlinear distortion cannot be reduced.

In view of the above point, the present invention obtains a conversion parameter by statistical processing based on the result obtained by actually measuring the position of the sample shot on the wafer to be processed in advance, and calculates this conversion parameter. In the alignment method of aligning each exposure shot on the wafer based on the calculated array coordinates calculated by using, it is possible to perform highly accurate alignment even when the wafer to be exposed has local non-linear distortion. The purpose is to do so.

[0014]

As shown in FIG. 4, for example, an alignment method according to the present invention is performed on the basis of array coordinates on a sample coordinate system (x, y) set on a substrate (W). (W) Plural processed regions (ES (i, j)) arranged on
In aligning each of these with a predetermined processing position in the stationary coordinate system (X, Y) that defines the movement position of the substrate (W), a plurality of processed regions (ES (i, j)) Of at least three preselected sample areas (SA (1) ~
By measuring the coordinate position of the SA (3)) on the stationary coordinate system (X, Y) and statistically calculating the measured coordinate positions, a plurality of processed regions (S) on the substrate (W) are obtained.
The array coordinates of each of A (1) to SA (3) on the static coordinate system (X, Y) are calculated, and the calculated plurality of processed regions (SA (1) to SA (3)) are calculated. The present invention relates to a method of aligning each of a plurality of processed regions (ES (i, j)) with respect to the processing position by controlling the moving position of the substrate (W) according to each array coordinate.

Then, according to the present invention, the first step of obtaining the amount of strain inside each of the plurality of processed regions (ES (i, j)) on the substrate (W) and each processed region of the plurality of processed regions. Processing area (E
In S (i, j)), the sample according to the integrated value of the strain amount obtained in the first step between this processed region and its sample region (SA (1) to SA (3)) Area (SA (1) ~
A second weighting factor is assigned to each SA (3))
A step and a third step of measuring the coordinate position of each of these sample areas on the static coordinate system (X, Y),
Sample coordinate system (x, y) of each sample area
It was obtained by multiplying the square of the difference between the array coordinate on the static coordinate system (X, Y) obtained from the above array coordinate using a set of conversion parameters and the measured coordinate position by the weighting coefficient. The error component is added to all of the sample areas, and the residual error component obtained is minimized so that one set of each of the plurality of processed areas (ES (i, j)) is processed. Using the fourth step of determining the value of the conversion parameter and the set of conversion parameter values obtained for each processing region (ES (i, j)), a plurality of processing targets on the substrate (W) are processed. And a fifth step of calculating array coordinates on the stationary coordinate system (X, Y) of each area.

[0016]

According to the present invention, the alignment is performed by the weighted EGA method, but when a set of conversion parameters is obtained for each processed region (ES (i, j)) on the substrate (W). , The value of the weighting factor given to each sample area (SA (1) to SA (3)) is determined according to the distortion state of the substrate (W).

That is, for example, the amount of local strain on the substrate (W) is obtained from the measurement result of the coordinate position of the sample area, and the processed area (ES (i, j)) to be exposed and each sample area are obtained. A weighting factor is assigned according to the integral value of the distortion amount between (SA (1) to SA (3)). Then, using one set of conversion parameters for each processing area (ES (i, j)), the array coordinate on the sample coordinate system (x, y) is used to determine the stationary coordinate system (X,
The array coordinates on Y) are calculated, and the processed region (ES (i, j)) is aligned based on the calculated array coordinates.

[0018]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the alignment method according to the present invention will be described below with reference to the drawings. FIG. 1 shows a schematic configuration of a projection exposure apparatus to which the alignment method of the present embodiment is applied. In FIG. 1, the illumination light IL generated from an extra-high pressure mercury lamp 1 is reflected by an elliptical mirror 2 and its illumination light IL is reflected. After focusing once at the second focus, collimator lens, interference filter, optical integrator (fly-eye lens)
And an illumination optical system 3 including an aperture stop (σ stop) and the like. Although not shown, the fly-eye lens is arranged in the in-plane direction perpendicular to the optical axis AX so that the reticle-side focal plane of the fly-eye lens substantially coincides with the Fourier transform plane (pupil conjugate plane) of the reticle pattern.

A shutter (for example, a four-blade rotary shutter) 37 for closing and opening the optical path of the illumination light IL by a motor 38 is arranged near the second focal point of the elliptic mirror 2. As the illumination light for exposure, laser light such as an excimer laser (KrF excimer laser, ArF excimer laser) or a harmonic wave of a metal vapor laser or a YAG laser is used in addition to the bright line of the ultra-high pressure mercury lamp 1 or the like. It doesn't matter.

In FIG. 1, illumination light (i-line or the like) IL in a wavelength range where the resist layer emitted from the illumination optical system 3 is exposed to light.
Is reflected by the beam splitter 4, and then passes through a first relay lens 5, a variable field stop (reticle blind) 6 and a second relay lens 7, and a mirror 8
Leading to. Then, the illumination light IL reflected by the mirror 8 in a substantially vertically downward direction illuminates the pattern area PA of the reticle R with substantially uniform illuminance via the main condenser lens 9. The arrangement surface of the reticle blind 6 and the pattern formation surface of the reticle R are in a conjugate relationship (image formation relationship), and the drive system 36
Thus, the illumination field of the reticle R can be arbitrarily set by opening and closing the plurality of movable blades that form the reticle blind 6 to change the size and shape of the opening.

In the reticle R of the present embodiment, reticle marks serving as alignment marks are formed at substantially central portions of the four sides of the pattern area PA surrounded by the light-shielding band. By projecting the images of these reticle marks onto the resist layer of the wafer W, the images of these reticle marks are formed as latent images on the resist layer. Further, in this embodiment, those reticle marks are
It is also used as an alignment mark when aligning each reticle R with each shot area of the wafer W. The four reticle marks have the same structure (however, the directions are different). For example, a certain wafer mark for the X axis is, for example, a diffraction grating mark composed of seven dot marks arranged in the Y direction. , Are multi-marks arranged in five rows at predetermined intervals in the X direction. The wafer marks are formed by a light-shielding portion such as chrome inside a transparent window provided in the light-shielding band of the reticle R. Further, on the reticle R, alignment marks composed of two cross-shaped light-shielding marks are formed facing each other in the vicinity of the outer periphery of the reticle R. These two alignment marks are used for alignment of the reticle R (positioning with respect to the optical axis AX of the projection optical system 13).

The reticle R is mounted on a reticle stage RS which can be finely moved in the direction of the optical axis AX of the projection optical system 13 by a motor 12, and can be two-dimensionally moved and finely rotated in a horizontal plane perpendicular to the optical axis AX. It is placed. At the end of the reticle stage RS, a movable mirror 11m that reflects a laser beam from a laser light wave interferometer (laser interferometer) 11
Is fixed, and the two-dimensional position of the reticle stage RS is constantly detected by the laser interferometer 11 with a resolution of, for example, about 0.01 μm. Reticle alignment systems (RA systems) 10A and 10B are arranged above the reticle R, and these RA systems 10A and 10B are mounted on the reticle R.
Two cross-shaped alignment marks formed near the outer periphery of the are detected. By finely moving the reticle stage RS based on the measurement signals from the RA systems 10A and 10B, the reticle R is positioned so that the center point of the pattern area PA coincides with the optical axis AX of the projection optical system 13.

The illumination light IL that has passed through the pattern area PA of the reticle R enters the projection optical system 13 that is telecentric on both sides, and is projected by the projection optical system 13 to a projected image of the circuit pattern of the reticle R that is reduced to 1/5. However, a resist layer is formed on the surface, and the surface is projected (imaged) so as to be superposed on one shot area on the wafer W held so that the surface substantially coincides with the best imaging plane of the projection optical system 13. .

The wafer W is vacuum-sucked by a finely rotatable wafer holder (not shown), and is held on the wafer stage WS via this wafer holder. The wafer stage WS is configured to be two-dimensionally movable in a step-and-repeat manner by a motor 16,
When the transfer exposure of the reticle R onto one shot area is completed, the wafer stage WS is stepped to the next shot position. A movable mirror 15 that reflects the laser beam from the laser interferometer 15 is provided at the end of the wafer stage WS.
m is fixed, and the two-dimensional coordinates of the wafer stage WS are constantly detected by the laser interferometer 15 with a resolution of about 0.01 μm, for example. The laser interferometer 15 is
The coordinates of one direction perpendicular to the optical axis AX of the projection optical system 13 of the wafer stage WS (referred to as the X direction) and the Y direction perpendicular thereto are measured, and the coordinates in the X direction and the Y direction are measured. A stage coordinate system (stationary coordinate system) (X, Y) of wafer stage WS is defined. That is, the coordinate value of the wafer stage WS measured by the laser interferometer 15 is the coordinate value on the stage coordinate system (X, Y).

On the wafer stage WS, a reference member (glass substrate) 14 provided with a reference mark used when measuring a baseline amount (described later) or the like has almost the same height as the exposed surface of the wafer W. Is provided. The reference member 14 has, as a reference mark, a slit pattern composed of five light-transmitting L-shaped patterns and two sets of reference patterns formed of light-reflecting chrome (duty ratio is 1:
1) and are provided. One set of reference patterns is
A diffraction grating mark formed by arranging 7 dot marks arranged in the Y direction in three rows in the X direction, a diffraction grating mark formed by arranging three linear patterns in the X direction, and 12 extending in the Y direction. The bar marks of the book are arranged in the X direction. The other set of reference patterns is the one set of reference patterns rotated by 90 °.

The illumination light (exposure light) transmitted below the reference member 14 using an optical fiber (not shown) or the like causes the slit pattern formed on the reference member 14 from below (inside the wafer stage WS). It is configured to be illuminated. The illumination light transmitted through the slit pattern of the reference member 14 forms a projected image of the slit pattern on the back surface (pattern surface) of the reticle R via the projection optical system 13. Further, the illumination light that has passed through any of the four reticle marks on the reticle R will be reflected by the main condenser lens 9,
The illumination light that has reached the beam splitter 4 through the relay lenses 7, 5 and the like and has passed through the beam splitter 4 is arranged in the vicinity of the pupil conjugate plane of the projection optical system 13 and the photoelectric detector 3 is arranged.
The light is received by 5. The photoelectric detector 35 outputs a photoelectric signal SS corresponding to the intensity of the illumination light to the main control system 18. Hereinafter, the optical fiber (not shown), the reference member 14, and the photoelectric detector 35 are collectively referred to as an ISS (Imaging Slit Sensor) system.

Further, in FIG. 1, an image formation characteristic correction unit 19 capable of adjusting the image formation characteristic of the projection optical system 13 is also provided.
The imaging characteristic correction unit 19 in this embodiment is the projection optical system 1
Some of the lens elements that make up part 3, especially reticle R
By independently driving (moving or tilting in a direction parallel to the optical axis AX) each of the plurality of lens elements close to each other by using a piezoelectric element such as a piezo element, For example, it corrects projection magnification and distortion.

Next, an off-axis type alignment sensor (hereinafter referred to as "Field Imag") is provided on the side of the projection optical system 13.
e Alignment system (FIA system) ”is provided. In this FIA system, the light generated by the halogen lamp 20 is converted into the condenser lens 21 and the optical fiber 22.
It is guided to the interference filter 23 through the light source, and the light in the photosensitive wavelength region and the infrared wavelength region of the resist layer is cut off there. The light transmitted through the interference filter 23 enters the telecentric objective lens 27 via the lens system 24, the beam splitter 25, the mirror 26 and the field stop BR. The light emitted from the objective lens 27 is reflected by a prism (or mirror) 28 fixed around the lower part of the lens barrel of the projection optical system 13 so as not to block the illumination visual field of the projection optical system 13, and the wafer W is almost vertical. To irradiate.

The light from the objective lens 27 is applied to a partial area including the wafer mark (base mark) on the wafer W, and the light reflected from the area is the prism 28, the objective lens 27, the field stop BR, and the mirror 26. , Is guided to the index plate 30 via the beam splitter 25 and the lens system 29. Here, the index plate 30 is arranged in a plane conjugate with the wafer W with respect to the objective lens 27 and the lens system 29, and the image of the wafer mark on the wafer W is formed in the transparent window of the index plate 30. Further, the index plate 30 is formed with two linear marks extending in the Y direction at predetermined intervals in the X direction as index marks in the transparent window.
The light that has passed through the index plate 30 receives the first relay lens system 31,
The image of the wafer mark and the image of the index mark are formed on the light receiving surface of the image pickup device 34 by being guided to the image pickup device (CCD camera etc.) 34 via the mirror 32 and the second relay lens system 33. The image pickup signal SV from the image pickup device 34 is supplied to the main control system 1
8, the position (coordinate value) of the wafer mark in the X direction is calculated. Although not shown in FIG. 2, in addition to the FIA system having the above configuration (FIA system for X axis),
Another set of FIA for detecting mark position in Y direction
A system (FIA system for Y axis) is also provided.

Next, TT is provided on the upper side of the projection optical system 13.
An L (through the lens) type alignment sensor 17 is also arranged, and the position detection light from the alignment sensor 17 is transmitted through the mirrors M1 and M2 to the projection optical system 1.
It is led to 3. The light for detecting the position is the projection optical system 1
The wafer W on the wafer W is irradiated with the reflected light from the wafer W via the projection optical system 13, the mirror M2, and the mirror M1, and the alignment sensor 17
Returned to. The alignment sensor 17 obtains the position of the wafer mark on the wafer W from the signal obtained by photoelectrically converting the returned reflected light.

FIG. 2 shows a detailed structure of the TTL type alignment sensor 17 in FIG. 1. In FIG. 2, the alignment sensor 17 of this example is a two-beam interference type alignment system (hereinafter referred to as “LIA system”). ) And a laser step alignment type alignment system (hereinafter referred to as “LSA system”), and the optical members thereof are maximally shared. Although briefly described here, a more specific configuration is disclosed in Japanese Patent Laid-Open No. 2-272305.

In FIG. 2, a laser beam emitted from a light source (He-Ne laser light source, etc.) 40 is split by a beam splitter 41, and the laser beam reflected here is passed through a shutter 42 to a first beam shaping optical system. (LI
A optical system) 45. On the other hand, the laser beam transmitted through the beam splitter 41 enters the second beam shaping optical system (LSA optical system) 46 via the shutter 43 and the mirror 44. Therefore, the shutters 42 and 43
Can be used by switching between the LIA system and the LSA system by appropriately driving.

The LIA optical system 45 includes two sets of acousto-optic modulators, etc., and emits two laser beams having a predetermined frequency difference Δf substantially symmetrically with respect to the optical axis.
Further, the two laser beams emitted from the LIA optical system 45 reach the beam splitter 49 via the mirror 47 and the beam splitter 48, and the two laser beams transmitted therethrough are a lens system (inverse Fourier transform lens). 5
The light enters the reference diffraction grating 55, which is fixed on the apparatus, from two different directions at a predetermined crossing angle, and forms an image (crossing) through the mirror 3 and the mirror 54. The photoelectric detector 56 receives the interference light of the diffracted lights that are transmitted through the reference diffraction grating 55 and generated in substantially the same direction, and outputs a sinusoidal photoelectric signal SR corresponding to the intensity of the diffracted light to the main control system 18 (FIG. 2))
It is output to the A arithmetic unit 58.

On the other hand, the two laser beams reflected by the beam splitter 49 intersect once at the opening of the field stop 51 by the objective lens 50, and then the mirror M2 (see FIG. 1).
The inside mirror M1 is incident on the projection optical system 13 via a mirror (not shown). Further, the two laser beams incident on the projection optical system 13 become substantially symmetrical with respect to the optical axis AX on the pupil plane of the projection optical system 13 and once converged in a spot shape. The parallel luminous fluxes are inclined with respect to the direction (Y direction) with respect to each other with the optical axis AX in between, and become parallel luminous fluxes, which are incident on the wafer mark from two different directions at a predetermined crossing angle. A one-dimensional interference fringe that moves at a speed corresponding to the frequency difference Δf is formed on the wafer mark, and the ± first-order diffracted light (interference light) generated in the same direction from the mark, that is, the optical axis direction in this case, is projected by the projection optical system. The light is received by the photoelectric detector 52 via the system 13, the objective lens 50, etc., and the photoelectric detector 52 receives the sine-wave photoelectric signal S corresponding to the cycle of the change in brightness of the interference fringes.
Dw is output to the LIA operation unit 58. The LIA calculation unit 58 calculates the position shift amount of the wafer mark from the phase difference on the waveforms of the two photoelectric signals SR and SDw, and uses the position signal PDs from the laser interferometer 15 to determine the position shift amount. The coordinate position of the wafer stage WS when it becomes zero is obtained, and this information is output to the alignment data storage unit 61 (see FIG. 3).

The LSA optical system 46 includes a beam expander, a cylindrical lens and the like, and the laser beam emitted from the LSA optical system 46 enters the objective lens 50 via the beam splitters 48 and 49. Further, the laser beam emitted from the objective lens 50 once converges into a slit shape at the opening of the field stop 51, and then enters the projection optical system 13 via the mirror M2. The laser beam incident on the projection optical system 13 passes through almost the center of its pupil plane, then extends in the X direction within the image field of the projection optical system 13 and is directed to the optical axis AX as an elongated strip-shaped spot light on the wafer. Projected onto W.

When the spot light and the wafer mark (diffraction grating mark) on the wafer W are moved relative to each other in the Y direction, the light generated from the wafer mark passes through the projection optical system 13, the objective lens 50 and the like and is a photoelectric detector. The light is received at 52. The photoelectric detector 52 has ± 1st order of the light from the wafer mark.
Only the third-order diffracted light is photoelectrically converted, and the photoelectric signal SDi corresponding to the light intensity obtained by photoelectrically converting in this manner is used as the main control system
It is output to the LSA calculation unit 57 in the inside. The LSA arithmetic unit 57 has a position signal PDs from the laser interferometer 15.
Also, the LSA calculation unit 57 samples the photoelectric signal SDi in synchronization with the up / down pulse generated for each unit movement amount of the wafer stage WS. Furthermore, LS
The A calculation unit 57 converts each sampling value into a digital value and stores it in the memory in the order of addresses, and then calculates the position of the wafer mark in the Y direction by a predetermined calculation process, and stores this information in the alignment data storage of FIG. It is output to the unit 61.

Next, the structure of the main control system 18 of FIG. 1 will be described with reference to FIG. FIG. 3 shows the main control system 18 of this example and the members related thereto, and in FIG.
Arithmetic unit 57, LIA arithmetic unit 58, FIA arithmetic unit 59, alignment data storage unit 61, EG
A calculation unit 62, storage unit 63, shot map data unit 64, system controller 65, wafer stage controller 66, and reticle stage controller 6
A main control system 18 is composed of 7. Among these members, the LSA arithmetic unit 57 and the LIA arithmetic unit 5
8 and the FIA operation unit 59 obtains the coordinate position of each wafer mark in the stage coordinate system (X, Y) from the corresponding photoelectric signal, and supplies the obtained coordinate position to the alignment data storage unit 61. Alignment data storage unit 61
Information on the measured coordinate position in the EGA calculation unit 6
2 is supplied.

The shot map data storage unit 64 stores the designed array coordinate values of the wafer marks belonging to each shot area on the wafer W in the coordinate system (x, y) on the wafer W. The array coordinate value of is also supplied to the EGA calculation unit 62. Based on the measured coordinate values and the designed coordinate values, the EGA calculation unit 62 uses the least squares method to convert the designed array coordinate values in the coordinate system (x, y) on the wafer W into the stage coordinate system (X , Y) to obtain six conversion parameters (corresponding to the conversion parameters a to f of (Equation 1)) for calculating the calculated array coordinate value,
The conversion parameters a to f are supplied to the storage unit 63.

At this time, the system controller 65
The LSA arithmetic unit 57, the LIA arithmetic unit 58, and the FIA arithmetic unit 59 are caused to calculate the coordinate position of the wafer mark, and the EGA arithmetic unit 62 determines the conversion parameters a to f, respectively, in accordance with this. Further, the EGA calculation unit 62 uses the conversion parameters a to f stored in such a manner to convert the designed array coordinate values in the coordinate system (x, y) on the wafer W into the stage coordinate system (X, Y). The calculated array coordinate value is calculated and the calculated array coordinate value is supplied to the system controller 65.

In response to this, the system controller 65
1 drives the wafer stage WS of FIG. 1 via the motor 16 while monitoring the measurement value of the laser interferometer 15 via the wafer stage controller 66 to position each shot area on the wafer W and to perform each shot area. Exposure to. The system controller 65 also controls the laser interferometer 11 via the reticle stage controller 67.
1 while monitoring the measured value of
The reticle stage RS is driven to adjust the position of the reticle R.

Next, an operation for positioning each shot area on the wafer W and projecting and exposing the pattern image of the reticle R on each shot area in this example will be described. First, the arrangement of shot areas on the wafer W and the shape of a wafer mark as an alignment mark will be described. Figure 4
4A shows an arrangement of shot areas on the wafer W. In FIG. 4A, the exposure target is regularly arranged on the wafer W along the coordinate system (x, y) set on the wafer W. Shot area (exposure shot) ES (3,1), ES (4,1),
.., ES (4,6) are formed, and each exposure shot ES (i,
Chip patterns are formed in j) by the previous steps. Further, each exposure shot ES (i, j) is separated by a street line having a predetermined width in the x direction and the y direction, and the center of the street line extending in the x direction close to each exposure shot ES (i, j). A wafer mark for the X direction is formed as an alignment mark at the portion, and a wafer mark for the Y direction is formed at the center of the street line extending in the y direction near each exposure shot ES (i, j). Among these wafer marks, FIG. 4A shows a wafer mark Mx1 for the X direction and a wafer mark My1 for the Y direction. The wafer marks Mx1 and My1 are formed by arranging three linear patterns at a predetermined pitch in the x direction and the y direction, respectively, and these patterns are formed in the lower portion of the wafer W as concave or convex patterns.

When exposing the wafer W, eight shot areas shown by hatching are selected from the exposure shots ES (i, j). Sample shots SA (1) to SA are selected from the shot areas thus selected.
Assuming (8), the wafer marks for the X direction and the Y direction are formed close to each sample shot SA (i). In this example, each sample shot SA (1) is measured by measuring the positions of these wafer marks.
~ Measure the coordinate position of SA (8) on the stage coordinate system (X, Y). Specifically, the image pickup signal of the wafer mark Mx1 is supplied to, for example, the FIA calculation unit 59 of FIG. 3 via the image pickup device 34 of FIG. 1, and the FIA calculation unit 59 sets the wafer mark Mx1 under the set measurement parameter. The position detection in the X direction is performed.

FIG. 5 shows a state of the wafer mark Mx1 imaged by the FIA type image pickup device 34 of FIG. 2, and the image pickup signal obtained at that time is stored in the waveform data storage circuit 60 of FIG. As shown in FIG. 5, within the imaging visual field VSA of the image sensor 34, a wafer mark Mx1 having three linear patterns and an index mark FM1 formed on the index plate 30 of FIG. 1 so as to sandwich the wafer mark Mx1. , FM2 are arranged. The image sensor 34 electrically scans the images of the wafer mark Mx1 and the index marks FM1 and FM2 along the horizontal scanning line VL. At this time, since only one scanning line is disadvantageous in terms of SN ratio, it is possible to add and average the levels of the imaging signals obtained by a plurality of horizontal scanning lines within the imaging visual field VSA for each pixel in the horizontal direction. desirable. As a result, the position of the wafer mark Mx1 in the X direction is measured, and similarly, the position of the wafer mark My1 in the Y direction is measured by the FIA system for the Y direction.

FIG. 4 (b) shows another example of the wafer mark. In FIG. 4 (b), a wafer mark MAX formed of a diffraction grating pattern having a predetermined pitch with respect to the measurement direction X is formed. Has been done. This wafer mark M
In order to detect the position of Ax, the two laser beams BM ₁ and BM ₂ emitted from the LIA optical system 45 (see FIG. 2) in the alignment sensor 17 of FIG. Irradiate on. Its pitch in the X direction of the crossing angle and the wafer mark MAx is the laser beam BM ₁ -1 order diffracted light B ₁ from the wafer mark MAx by (-1) and the laser beam BM ₂ +1 order diffracted light B ₂ from the wafer mark MAx by (+) Is set to be parallel. The interference light of the -1st-order diffracted light B ₁ (-1) and the + _1st-order diffracted light B ₂ (+) is converted into a photoelectric signal SDw by the photoelectric detector 52 in FIG. 2, and the photoelectric signal SDw is supplied to the LIA operation unit 58. In the LIA arithmetic unit 58,
The amount of misalignment of the wafer mark MAx in the X direction is calculated from the phase difference between the photoelectric signal SR as the reference signal and the photoelectric signal SDw.

FIG. 4C shows still another example of the wafer mark. In FIG. 4C, the dot marks are arranged at a predetermined pitch in the Y direction perpendicular to the X direction which is the measurement direction. The wafer mark MBy is formed.
To detect the position of the wafer mark MBy, the LSA optical system 46 (see FIG. 2) in the alignment sensor 17 of FIG.
The laser beam emitted from the laser beam is emitted as slit-shaped spot light LYS long in the Y direction near the wafer mark MBy. Then, when the wafer stage WS of FIG. 1 is driven and the wafer mark MBy is scanned with respect to the spot light LYS, in a range in which the spot light LYS scans the wafer mark MBy, the wafer mark MBy is moved in a predetermined direction from the wafer mark MBy. Diffracted light is emitted to. A photoelectric signal SDi obtained by photoelectrically converting the diffracted light by the photoelectric detector 52 of FIG. 2 is supplied to the LSA operation unit 57, and LS
The A calculation unit 57 obtains the position of the wafer mark MBy in the X direction based on the set measurement parameter.

Next, an example of the entire operation when the pattern image of the reticle R is exposed on each exposure shot ES (i, j) of the wafer W of FIG. 4A by the projection exposure apparatus of this example will be described. . In this example, a method of giving a weighting constant is devised by a weighted EGA (enhanced global alignment) method. First, the coordinate values of the wafer marks belonging to the eight sample shots SA (1) to SA (8) in FIG. 4A in the stage coordinate system (X, Y) are measured.
As the measurement sensor in this case, for example, an FIA system including the image sensor 34 of FIG. 1 is used, but depending on the shape of the wafer mark, an LIA system or an LSA system is also used. The measured coordinate values are supplied to the EGA calculation unit 62 via the alignment data storage unit 61 of FIG.
The A calculation unit 62 obtains the values of the six conversion parameters a to f satisfying (Equation 1) from the designed and measured coordinate values of the wafer mark using the weighted least squares method. . This is a calculation called weighted EGA calculation.

Specifically, when the W1-EGA method, which is the first method among the weighted EGA methods, is used, the calculated coordinate position of the exposure shot ES (i, j) on the wafer W is calculated. When determining, this exposure shot and m (in FIG. 4, m =
8) Measured coordinate positions (alignment data) of these m sample shots according to the distances LK1 to LK8 between the sample shots SA (1) to SA (8).
Is given a weight W _{ij n} . Therefore, the residual error component Eij is defined as follows.

[0048]

[Equation 2]

Then, the values of the conversion parameters a to f of (Equation 1) are determined so that the residual error component Eij defined in this way is minimized. Note that here, sample shots SA (1) to be used for each exposure shot ES (i, j)
SA (8) is the same, but naturally each exposure shot ES
The distance to each sample shot SA (n) is different for each (i, j). Therefore, the weight W _ijn given to the coordinate position (alignment data) of the sample shot SA (n) changes for each exposure shot ES (i, j). Then, by determining the conversion parameters a to f for each exposure shot ES (i, j) and calculating the coordinate position on the basis of (Equation 1), the calculation array of all the exposure shots on the wafer W is calculated. The coordinates (shot array) are determined.

Thus, in the W1-EGA method, the wafer W is
The weight W _ijn for the coordinate data of each sample shot SA (n) changes for each exposure shot ES (i, j) above. As an example, the weight W _{ijn is set} to the exposure shot ES
It is expressed as a function of the distance LKn between (i, j) and the nth sample shot SA (n) as follows. However, the parameter S is a parameter for changing the degree of weighting.

[0051]

[Equation 3]

As is clear from this equation, the exposure shot E
Sample shot SA with short distance LKn to S (i, j)
(N), the weight W _ijn given to the alignment data
Is becoming larger. Further, in (Equation 3), when the value of the parameter S is sufficiently large, the result of the statistical calculation process is almost equal to the result obtained by the normal EGA method. On the other hand, when all the exposure shots ES (i, j) on the wafer are sample shots SA (n) and the value of the parameter S is made sufficiently close to zero, the position of the wafer mark is measured for each shot area to perform the alignment. This is almost the same as the result obtained by the so-called die-by-die method. That is, W1-
In the EGA method, by setting the parameter S to an appropriate value, an intermediate effect between the EGA method and the die-by-die method can be obtained.

The value of the parameter S is given as an example as follows. In this equation, D is a weighting parameter, and the operator sets the value of the weighting parameter D to a predetermined value to automatically determine the parameter S, and thus the weighting W _ijn .

[0054]

S = D ² / (8 · log _e 10) The physical meaning of this weight parameter D is that the range of sample shots effective for calculating the coordinate position of each shot area on the wafer (hereinafter, simply "Zone").
That is, when the zone is large, the number of effective sample shots is large, and the result is close to the result obtained by the conventional EGA method. On the contrary, when the zone is small, the number of valid sample shots is small, and the result is close to the result obtained by the die-by-die method.

The equation for determining the parameter S is not limited to (Equation 4), and the following (Equation 5) can be used, for example. However, the area of the wafer is A [mm ² ], the number of sample shots is m, and the correction coefficient (positive real number) is C.

[0056]

[Equation 5] S = A / (m · C) This (Equation 5) reflects the change in the wafer size (area) and the number of sample shots in the determination of the parameter S, and is a correction coefficient to be used in the determination. The optimum value of C does not fluctuate too much. When the correction coefficient C is small, the value of the parameter S is large, and the value is close to the result obtained by the conventional EGA method. When the correction coefficient C is large, the value of the parameter S is small. Close to the results obtained with the method. Therefore, only by inputting the correction coefficient C previously determined by experiments or simulations to the exposure apparatus via the operator or the identification code reader, the degree of weighting of the alignment data from (Equation 5), that is, (Equation 3) The weight W _ijn determined by is automatically determined.

The second weighted EGA system (W2-EGA system) may be used instead of the W1-EGA system. In this W2-EGA method, the distance (radius) between the deformation center point of the wafer W (the point symmetry center of the nonlinear distortion), that is, the wafer center and the exposure shot ES (i, j) on the wafer W is LEij. , Wafer center and m (m = 8 in the figure) sample shots SA (1) to SA
The distance (radius) between each of (8) is LW1 to LW
8 And even in this W2-EGA method, W1-
Similar to the EGA method, the distance LEij and the distances LW1 to LW
Eight sample shots SA (1) to S (S) depending on W8
A weight W _ijn ′ defined by the following equation is given to each of the alignment data of A (8).

[0058]

[Equation 6]

As the parameter S in this (Equation 6), the parameter S in (Equation 4) or (Equation 5) is also used. Then, the weight W _ijn of the weight W _ijn '(number 2)
Instead of, the conversion parameters a to f are determined so that the residual error component Eij of (Equation 2) is minimized.
After that, the EGA calculation unit 62 uses the conversion parameters a to f and the exposure shots ES (i, j) obtained as described above.
Substituting the designed array coordinate value of (1) into (Equation 1), the calculated array coordinate value of each exposure shot ES (i, j) is obtained.

Next, the amount of distortion in each exposure shot ES (i, j) is obtained from the calculated array coordinate values thus obtained. Specifically, as shown in FIG. 6A, with respect to the exposure shot ES (i, j), exposure shots ES (i-
1, j), ES (i + 1, j) and upper and lower exposure shots ES (i, j +
1), ES (i, j-1) will be described for the case where the positional deviation amount (vector) between the designed coordinate value and the calculated coordinate value is as follows. Positional deviation of exposure shot ES (i, j): (P1, Q
1) Amount of displacement of exposure shot ES (i-1, j): (P2, Q
2) Positional deviation of exposure shot ES (i + 1, j): (P3, Q
3) Positional deviation of exposure shot ES (i, i-1): (P4, Q
4) Position shift amount of exposure shot ES (i, i + 1): (P5, Q
5)

As shown in FIG. 6B, using the measurement results, the distortion Dij inside each exposure shot ES (i, j) is calculated as follows by the distortion vector <Dijx> in the X direction and the Y direction. , And the distortion vector <Digy> is defined.

[0062]

Dij = (<Dijx>, <Dijy>) In this case, the distortion vector <Dijx> in the X direction and the distortion vector <Dijy> in the Y direction are as follows.

[0063]

[Expression 8] <Dijx> = ((P2 + P3-2 × P1) / 2, (Q2 + Q3-2 × Q1) / 2) <Dijy> = ((P4 + P5-2 × P1) / 2, (Q4 + Q5-2 × Q1) / 2) That is, the vector from the center of the exposure shot ES (i, j) to the midpoint CX of the exposure shot ES (i, j) on both sides in the X direction is X. Direction distortion vector <Dijx>
And the vector from the center of the exposure shot ES (i, j) with respect to the midpoint CY of the exposure shots on both sides of the exposure shot ES (i, j) in the Y direction is the distortion vector <Dij in the Y direction.
x>.

Also, the exposure shot ES (i, j) is the wafer W.
If there is no upper, lower, left, or right exposure shot and the distortion cannot be calculated, the value of the distortion of the adjacent exposure shot is used instead. For example, in the exposure shot on the left end of the wafer W, the X component of the distortion of the exposure shot on the right side of the shot is taken as the distortion vector in the X direction of the shot. In this case, since the normal calculation can be performed for the component in the Y direction, the actual calculated value is used.

Next, a straight line connecting the distortion Dij inside each exposure shot ES (i, j) and the exposure shot ES (p, q) and the sample shot SA (k) is the inside of each exposure shot. The distortion amount D (pqk) between the sample shot SA (k) and the exposure shot ES (p, q) is obtained as the sum of products of lengths L (i, j) passing through. That is, the distortion amount D (pq
k) is divided into a vector in the X direction and a vector in the Y direction as follows.

[0066]

## EQU9 ## D (pqk) = (<Dx (pqk)>, <Dy
(Pqk)>) In this case, the vector <Dx (pqk)> in the X direction and the vector <Dy (pqk)> in the Y direction are as follows.
However, the sum symbol Σ _ij represents the sum of the subscripts i and j.

[0067]

<Dx (pqk)> = Σ _ij L (i, j) <Dijx><Dy(pqk)> = Σ _ij L (i, j) <Dijy> where the distortion amount D (pqk) is When obtaining, the exposure shots are calculated assuming that they are regularly arranged on the wafer at a predetermined shot pitch. For example, as shown in FIG.
Sample shot SA for exposure shot ES (3,3)
Each component of the distortion amount D (333) of (3) <Dx (33
3)> and <Dy (333)> are as follows.

[0068]

[Equation 11] <Dx (333)> = L (1,3) <D13x>
+ L (2,3) <D23x> + L (3,3) <D33x>, <Dy (333)> = L (1,3) <D13y> + L (2,3)
<D23y> + L (3,3) <D33y>

In this example, the distortion amount D (pq
X component <Dx (pqk)> and Y component <Dy (p
qk)>) corresponding weights Wx (pqk) and Wy (pqk) to the residual error of each sample shot SA (k). An example of the weight Wx (k) is the difference between the predetermined constant C and the absolute value of the distortion amount component as follows.

[0070]

## EQU12 ## Wx (pqk) = C- | <Dx (pqk)> |
(C ≧ | <Dx (pqk)> |), Wx (pqk) = 0 (C <| <Dx (pqk)> |) The weight Wy (pqk) in the Y direction can also be expressed in the same form. . That is, the larger the distortion amount, the more weight Wx (pq
The values of k) and Wy (pqk) become smaller.

Using the weights Wx (pqk) and Wy (pqk), the X and Y components of the residual error of each sample shot SA (k) are weighted, and each exposure shot ES (p, q). ) Is calculated for EGA. That is, the residual error component Epq corresponding to (Equation 2) in this case is as follows.

[0072]

[Equation 13]

Then, the conversion parameters a to f of (Equation 1) are determined for each exposure shot ES (p, q) so as to minimize the residual error component, and the conversion parameters a to f are set.
And the designed coordinate values of the exposure shot, the calculated array coordinates on the stage coordinate system (X, Y) are obtained.
The baseline amount, which is the distance between the measurement center of the FIA, LIA, and LSA alignment sensors and the reference point in the exposure field of the projection optical system 13, is determined in advance. Therefore, the system controller 65
Is a reticle that sequentially positions each shot area ES (p, q) based on the calculated coordinate values obtained by correcting the array amount calculated by the EGA calculation unit 62 for the baseline amount. The pattern image of R is exposed.

The results of applying the method of this example to the wafer W having the distortion shown in FIG. In FIG. 8A, for example, in the exposure shot ES (i, j), the central point P
A straight line is drawn from 1 to the outer point P2, but the straight line is the exposure shot E due to various processes.
This means that the center of S (i, j) has moved from the design point P1 to the point P2. Therefore, the wafer W of FIG.
Indicates a strained state in which only the central portion locally extends in the radial direction.

For the wafer W shown in FIG.
As shown in (b), 13 shaded exposure shots are used as sample shots SA (1) to SA (13), and the residual error component is first aligned by a simple weighted EGA method represented by (Equation 2). I went. As a result, the residual error, which is the difference between the calculated array coordinate and the actual array coordinate for each exposure shot, is shown by a line segment in FIG. 8B.

On the other hand, in the case where the alignment is performed by the weighted EGA method in which the residual error component is represented by (Equation 13) and the weight is changed according to the distortion amount as in the present embodiment, FIG.
As shown in (c), the residual error of each exposure shot was extremely small, and the effect of improving the alignment accuracy was recognized. For example, with respect to the residual error vector δ1 of a certain exposure shot in FIG. 8B, the absolute value of the residual error vector δ2 of the corresponding exposure shot in FIG. 8C is significantly smaller.

The X component of the distortion amount D (pqk) <Dx
(Pqk)> and the Y component <Dy (pqk)>) as the setting method of the weights Wx (pqk) and Wy (pqk) are not limited to the above (Equation 12), for example, a predetermined constant C is used. Alternatively, the following function may be used.

[0078]

[Expression 14] Wx (pqk) = 1 / (C + | <Dx (pqk)> |) In general, the weights Wx (pqk) and Wy (pqk) are respectively the magnitudes of the distortion amounts | <Dx (pqk). > | And | <D
The function may be such that it decreases as y (pqk)> | increases.

Next, in order to obtain the amount of distortion in each exposure shot, in the above embodiment, the calculated array coordinates of each exposure shot were obtained from the measured coordinate values of the sample shot by the weighted EGA method. However, the method of obtaining the distortion amount in the exposure shot is not limited to the above method, and the following method may be used, for example. That is,
In FIG. 4, for each sample shot SA (i), the measured coordinates (Pi, Q
i) and the measured coordinates (P) of the center of another sample shot SA (j) in which the shot position in the X direction and the shot position in the Y direction differ from that shot by m and n shots, respectively.
j, Qj). After that, by linear interpolation between two points, the straight line connecting the center of the sample shot SA (i) and the center of the sample shot SA (j) and the shot center at the intersection of the side of the sample shot SA (i) The relative position difference (ΔXij, ΔYij) is calculated as follows.

[0080]

ΔXij = (Pj−Pi) / {(2m) ² +
(2n) ² } ^1/2 ΔYij = (Qj−Qi) / {(2m) ² + (2n)
² } ^1/2 The outer shape of the sample shot SA (i) is obtained using this result. Therefore, the relative position difference (ΔXij, ΔYi with respect to the shot center at the intersection of the straight line connecting the centers and the side).
j) (j = 1, 2, ..., 8; j ≠ i), weighting each relative position difference according to the inter-shot distance (for example, the reciprocal of the inter-shot distance), and calculating the X direction and the Y direction. Second-order least-squares approximation is performed for each axis of the direction, and sample shot SA
Find the coordinates of the side of (i).

From this result, sample shot SA
The difference in relative position between the shot center of (i), the center of each of the right side and the left side, and the difference in relative position between the center of the shot and each center of the upper side and the lower side are obtained, and the relative position The difference can be the intra-shot distortion.
In this way, the distortion in each sample shot is calculated, and the distortion amount of the remaining exposure shots (non-sample shots) may be calculated by linearly complementing the distortion amount of the sample shots.

Instead of determining the array coordinate for each shot by the weighted EGA method to obtain the distortion amount within the shot, the alignment sensor is used to detect the alignment marks attached to each of all the shot areas on the wafer. Then, the distortion amount in the shot may be obtained using the measured coordinates. It should be noted that the present invention is not limited to the above-described embodiments, and it goes without saying that various configurations can be adopted without departing from the gist of the present invention.

[0083]

According to the present invention, since the weighting coefficient assigned to the sample area is changed according to the integral value of the distortion amount between the processed area and the sample area, the local distortion in the substrate is suppressed. Even if it exists, there is an advantage that the alignment can be performed with high accuracy.

[Brief description of drawings]

FIG. 1 is a configuration diagram showing a projection exposure apparatus to which an embodiment of a positioning method according to the present invention is applied.

FIG. 2 is a TTL alignment sensor 1 shown in FIG.
7 is a block diagram showing a detailed configuration of No. 7.

3 is a block diagram showing a detailed configuration of a main control system 18 and the like in FIG.

4A is a plan view showing an arrangement of shot areas on a wafer exposed in the embodiment, FIG. 4B is an explanatory view of a wafer mark detection method for LIA system, and FIG. 4C is for LSA system. FIG. 3 is an explanatory diagram of a wafer mark detection method of FIG.

FIG. 5 is a diagram showing an observation region of an image sensor of an FIA type alignment sensor.

FIG. 6A is a diagram showing an array of shot regions used when obtaining distortion within a shot, and FIG. 6B is a diagram showing vectors corresponding to distortion within a shot.

FIG. 7 is an explanatory diagram for determining a weight for the sample shot SA (3).

FIG. 8A is a plan view showing an example of a wafer having a local distortion, and FIG. 8B is a residual error when alignment is performed by a weighted EGA method using a weight determined without depending on the distortion amount. FIG. 6C is a diagram showing a residual error when alignment is performed by a weighted EGA method using a weight determined according to the distortion amount.

[Explanation of symbols]

 1 Mercury lamp 3 Illumination optical system 9 Main condenser lens R Reticle 13 Projection optical system W Wafer WS Wafer stage 15 Laser interferometer 17 TTL type alignment sensor 18 Main control system ES (i, j) Exposure shot SA (1) to SA (8) Sample shot Mx1 wafer mark in X direction My1 wafer mark in Y direction

Claims (1)

[Claims] 1. A plurality of processed regions arranged on the substrate based on arrangement coordinates on a sample coordinate system set on the substrate are defined in a stationary coordinate system that defines a moving position of the substrate. Upon aligning with respect to a predetermined processing position, the coordinate position of at least three preselected sample areas in the stationary coordinate system among the plurality of processing areas is measured, and the plurality of measured coordinates are measured. By statistically calculating the position, the array coordinates on the stationary coordinate system of each of the plurality of processed regions on the substrate are calculated, and the substrate according to the calculated array coordinates of each of the plurality of processed regions. A method of aligning each of the plurality of processed regions with respect to the processing position by controlling a moving position, in which the inside of each of the plurality of processed regions on the substrate is The first step of obtaining the amount of misalignment, and the sample in each of the plurality of processed regions according to the integrated value of the amount of strain obtained in the first process between the processed region and the sample region. A second step of assigning a weighting factor to each of the areas; a third step of measuring the coordinate position of each of the sample areas on the stationary coordinate system; and an array of each of the sample areas on the sample coordinate system. An error component obtained by multiplying the square of the difference between the array coordinate on the stationary coordinate system obtained by using a set of conversion parameters from the coordinate and the measured coordinate position by the weighting coefficient,
A fourth step of determining the value of the one set of conversion parameters for each of the processed regions of the plurality of processed regions so that a residual error component obtained by adding all the sample regions in advance is minimized; A fifth step of calculating array coordinates on the stationary coordinate system of each of the plurality of processed regions on the substrate by using the values of the set of conversion parameters obtained for each of the processed regions.
A positioning method comprising: